MAR 15, 2019 | 11:45 AM
|WHERE:||The Graduate Center
365 Fifth Avenue
|WHEN:||March 15, 2019: 11:45 AM|
|CONTACT INFO:||Applied Topology|
|SPONSOR:||Data Science and Applied Topology Seminar|
Persistence diagrams have been widely recognized as a compact descriptor for characterizing multiscale topological features in data. When many datasets are available, statistical features embedded in those persistence diagrams can be extracted by applying machine learnings. In particular, the ability for explicitly analyzing the inverse in the original data space from those statistical features of persistence diagrams is significantly important for practical applications. In this paper, we propose a unified method for the inverse analysis by combining linear machine learning models with persistence images. The method is applied to point clouds and cubical sets, showing the ability of the statistical inverse analysis and its advantages.